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TECHNICAL PAPERS

A Fuzzy Adaptive Simplex Search Optimization Algorithm

[+] Author and Article Information
Mohamed B. Trabia

Department of Mechanical Engineering, University of Nevada, Las Vegas, Las Vegas, NV 89154-4027E-mail: mbt@me.unlv.edu

Xiao Bin Lu

Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV 89154-3005

J. Mech. Des 123(2), 216-225 (Oct 01, 1999) (10 pages) doi:10.1115/1.1347991 History: Received October 01, 1999
Copyright © 2001 by ASME
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References

Kosko, B., 1997, Fuzzy Engineering, Prentice Hall, Englewood Cliffs, New Jersey.
Rao,  S., 1986, “Description and Optimum Design of Fuzzy Mechanical Systems,” ASME J. Mech., Transm., Autom. Des., 108, pp. 1–7.
Diaz,  A., 1988, “Goal Aggregation in Design Optimization,” Eng. Optimiz., 13, pp. 257–273.
Wood,  K., Antonsson,  E., and Beck,  J., 1990, “Representing Imprecision in Engineering Design: Comparing Fuzzy and Probability Calculus,” Res. Eng. Des., 1, pp. 187–203.
Wood,  K., and Antonsson,  E., 1990, “Modeling Imprecision and Uncertainty in Preliminary Engineering Design,” Mech. Mach. Theory, 25, No. 3, pp. 305–324.
Thurston,  D., and Carnahan,  J., 1992, “Fuzzy Ratings and Utility Analysis in Preliminary Design Evaluation of Multiple Attributes,” ASME J. Mech. Des., 114, pp. 648–658.
Carnahan,  J., Thurston,  D., and Liu,  T., 1994, “Fuzzy Ratings for Multiattribute Design Decision-Making,” ASME J. Mech. Des., 116, pp. 511–521.
Vadde,  S., Allen,  J., and Mistree,  F., 1994, “Compromise Decision Support Problems for Hierarchical Design Involving Uncertainty,” Comput. Struct., 52, No. 4, pp. 645–658.
Ekel,  P., Pedrycz,  W., and Schizinger,  R., 1998, “A General Approach to Solving a Wide Class of Fuzzy Optimization Problems, Fuzzy Sets Syst., 97, pp. 49–66.
Ohkubo,  S., and Dissanayake,  P., 1999, “Multicriteria Fuzzy Optimization of Structural Systems, Int. J. Numer. Methods in Eng., 45, pp. 195–214.
Grignon, P., and Fadel, G., 1994, “Fuzzy Move Limit Evaluation in Structural Optimization,” AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, Florida.
Mulkay, E., and Rao, S., 1997, “Fuzzy Heuristics for Sequential Linear Programming,” Proceedings of the 1997 ASME Design Engineering Technical Conferences.
Spendley,  W., Hext,  G., and Himsworth,  F., 1962, “Sequential Application of Simplex Designs in Optimization and Evolutionary Operation,” Technometrics, 4, pp. 441.
Nelder,  J., and Mead,  R., 1965, “A Simplex Method for Function Minimization,” Comput. J., 7, pp. 308–313.
Rekalitis, G., Ravindaran, A., and Ragsdell, K., 1983, Engineering Optimization: Methods and Applications, Wiley-Interscience, New York.
Freudenstein,  F., and Roth,  B., 1963, “Numerical Solution of Systems of Nonlinear Equations,” J. ACM, 10, pp. 550–556.
More,  J., Garbow,  B., and Hillstron,  K., 1981, “Testing Unconstrained Optimization Software,” ACM Trans. Math. Softw., 7, pp. 17–41.
Fletcher,  R., and Powell,  M., 1963, “A Rapidly Convergent Descent Method for Minimization,” Comput. J. (UK), 6, pp. 163–168.
Powell,  M., 1964, “An Efficient Method for Finding the Minimum of a Function of Several Variables Without Calculating Derivatives,” Comput. J. (UK), 7, pp. 303–307.
Rao, S., 1996, Engineering Optimization: Theory and Practice, Wiley-Interscience, New York.
Teng, C., and Angeles, J., 1999, “A Sequential Quadratic-Programming Algorithm Using Orthogonal Decomposition with Gerschgorin Stabilization,” Proceedings of the 1999 ASME Design Engineering Technical Conferences.
Lo, C., and Papalambros, P., 1990, “A Deterministic Global Design Optimization Method for Nonconvex Generalized Polynomial Problems,” Advances in Design Automation, pp. 41–49, ASME, New York.

Figures

Grahic Jump Location
Reflection of the highest point in Nelder and Mead simplex algorithm
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Reflection of the highest point in fuzzy simplex algorithm
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Membership sets for the input of the fuzzy controller, Reflect
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Membership sets for the output of the fuzzy controller, Reflect
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Relation between the input and the output of the fuzzy controller, Reflect
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Membership sets for the first input of the fuzzy controller, Expand
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Membership sets for the second input of the fuzzy controller, Expand
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Membership sets for the output of the fuzzy controller, Expand
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Relation between the inputs and the output of the fuzzy controller, Expand
Grahic Jump Location
Membership sets for the input of the fuzzy controller, Contract
Grahic Jump Location
Membership sets for the output of the fuzzy controller, Contract
Grahic Jump Location
Relation between the input and output of the fuzzy controller, Contract
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Flowchart for the fuzzy simplex algorithm
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Contour plot of Beale’s Function
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Progression toward the minimum of Beale’s Function using Nedler and Mead Simplex
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Progression toward minimum of Beale’s Function using Fuzzy Simplex II
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Automatic screwdriver bit

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